7n^2+49n+47=-2-3n^2

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Solution for 7n^2+49n+47=-2-3n^2 equation: 


Simplifying
7n2 + 49n + 47 = -2 + -3n2

Reorder the terms:
47 + 49n + 7n2 = -2 + -3n2

Solving
47 + 49n + 7n2 = -2 + -3n2

Solving for variable 'n'.

Reorder the terms:
47 + 2 + 49n + 7n2 + 3n2 = -2 + -3n2 + 2 + 3n2

Combine like terms: 47 + 2 = 49
49 + 49n + 7n2 + 3n2 = -2 + -3n2 + 2 + 3n2

Combine like terms: 7n2 + 3n2 = 10n2
49 + 49n + 10n2 = -2 + -3n2 + 2 + 3n2

Reorder the terms:
49 + 49n + 10n2 = -2 + 2 + -3n2 + 3n2

Combine like terms: -2 + 2 = 0
49 + 49n + 10n2 = 0 + -3n2 + 3n2
49 + 49n + 10n2 = -3n2 + 3n2

Combine like terms: -3n2 + 3n2 = 0
49 + 49n + 10n2 = 0

Factor a trinomial.
(7 + 2n)(7 + 5n) = 0


Subproblem 1
Set the factor '(7 + 2n)' equal to zero and attempt to solve:

Simplifying
7 + 2n = 0

Solving
7 + 2n = 0

Move all terms containing n to the left, all other terms to the right.

Add '-7' to each side of the equation.
7 + -7 + 2n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 2n = 0 + -7
2n = 0 + -7

Combine like terms: 0 + -7 = -7
2n = -7

Divide each side by '2'.
n = -3.5

Simplifying
n = -3.5

Subproblem 2
Set the factor '(7 + 5n)' equal to zero and attempt to solve:

Simplifying
7 + 5n = 0

Solving
7 + 5n = 0

Move all terms containing n to the left, all other terms to the right.

Add '-7' to each side of the equation.
7 + -7 + 5n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 5n = 0 + -7
5n = 0 + -7

Combine like terms: 0 + -7 = -7
5n = -7

Divide each side by '5'.
n = -1.4

Simplifying
n = -1.4
Solution
n = {-3.5, -1.4}

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